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CBSE Class 11-science Answered

pls solve
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Asked by sdmbotch1123 | 18 Jan, 2023, 11:02: PM
answered-by-expert Expert Answer
 
begin mathsize 14px style fraction numerator left parenthesis 2 n right parenthesis factorial over denominator n factorial end fraction space equals space left parenthesis n plus 1 right parenthesis space left parenthesis n plus 2 right parenthesis space left parenthesis n plus 3 right parenthesis space..................... left parenthesis n plus n right parenthesis end style
 
begin mathsize 14px style fraction numerator left parenthesis 2 n right parenthesis factorial over denominator n factorial space n to the power of n end fraction space equals space fraction numerator left parenthesis n plus 1 right parenthesis space left parenthesis n plus 2 right parenthesis space left parenthesis n plus 3 right parenthesis space..................... left parenthesis n plus n right parenthesis over denominator n to the power of n end fraction end style
 
 
begin mathsize 14px style fraction numerator left parenthesis 2 n right parenthesis factorial over denominator n factorial space n to the power of n end fraction space equals space fraction numerator n to the power of n space open parentheses 1 plus 1 over n close parentheses space stretchy left parenthesis 1 plus 2 over n stretchy right parenthesis space stretchy left parenthesis 1 plus 3 over n stretchy right parenthesis space..................... stretchy left parenthesis 1 plus n over n stretchy right parenthesis over denominator n to the power of n end fraction end style
 
begin mathsize 14px style fraction numerator left parenthesis 2 n right parenthesis factorial over denominator n factorial space n to the power of n end fraction space equals space stretchy left parenthesis 1 plus 1 over n stretchy right parenthesis space stretchy left parenthesis 1 plus 2 over n stretchy right parenthesis space space stretchy left parenthesis 1 plus 3 over n stretchy right parenthesis space space..................... stretchy left parenthesis 1 plus n over n stretchy right parenthesis space equals space alpha end style
 
where α is a finite number
 
begin mathsize 14px style limit as n rightwards arrow infinity of space open parentheses fraction numerator left parenthesis 2 n right parenthesis factorial over denominator n factorial space n to the power of n end fraction close parentheses to the power of bevelled 1 over n end exponent space equals space limit as n rightwards arrow infinity of space alpha to the power of bevelled 1 over n end exponent end style
 
Let m = 1/n ;  if n → begin mathsize 14px style infinity end style  , then m → 0
 
begin mathsize 14px style space limit as n rightwards arrow infinity of space alpha to the power of 0 space equals space 1 end style
 
Answered by Thiyagarajan K | 19 Jan, 2023, 09:27: AM
CBSE 11-science - Maths
Asked by ns091764623 | 03 Mar, 2024, 08:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
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ANSWERED BY EXPERT ANSWERED BY EXPERT
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